General Modeling Framework Research Articles

Combining quantitative and qualitative reasoning in concurrent multi-player games

We propose a general framework for modelling and formal reasoning about multi-agent systems and, in particular, multi-stage games where both quantitative and qualitative objectives and constraints are involved. Our models enrich concurrent game models with payoffs and guards on actions associated with each state of the model and propose a quantitative extension of the logic {textsf {ATL}}^{*} that enables the combination of quantitative and qualitative reasoning. We illustrate the framework with some detailed examples. Finally, we consider the model-checking problems arising in our framework and establish some general undecidability and decidability results for them.

A general mixed-integer programming framework for efficient modeling, integration and optimization of thermodynamic cycle-based energy systems

Thermodynamic cycles are imperative systems for energy conversion, and optimization has been an important tool to improve their thermo-economic benefits. However, off-the-shelf software is often limited by long computational time, inflexibility for modeling and numerical difficulties. Here, we present an equation-based optimization framework featuring: (1) an inclusive modeling structure applicable to various thermodynamic cycles design problems; (2) versatile thermodynamic properties estimation for different working fluids; (3) capability of working fluids optimization with complex composition; (4) an efficient formulation method to model potential phase change of streams in simple/complicated heat exchangers; (5) a systematic optimization strategy to improve solution efficiency. The framework is formulated as mixed-integer nonlinear programming models, and its performance is demonstrated by two thermodynamic cycle optimization problems and one system design problem, including a supercritical CO2 Brayton cycle, cryogenic cycle (PRICO), and concentrated solar power (CSP) system. The Brayton cycle case serves as an illustrative example to show thermodynamic cycle design combining the consideration of stream properties calculation, unit operations, and flowsheet optimization. The PRICO example shows the efficacy of the proposed framework in simultaneously optimizing flowsheet and working fluids composition with complex heat exchangers and stream phase unknown a priori. The CSP case demonstrates that the framework can be extended to system optimization problems with high accuracy multi-parameter equation of state. Results prove that the framework is efficient and effective in solving thermodynamic cycle and related energy systems optimization problems.

Finite element modelling of defects in additively manufactured strut-based lattice structures

Strut-based lattice structures produced by powder bed fusion are prone to characteristic manufacturing defects that alter both their form and surface texture. Most studies in the literature focus on a subset of commonly observed defects, typically radius variation and strut waviness; surface defects remain relatively unexplored. Furthermore, there remains a need for the development of a general finite element modelling framework that can implement a range of defects into any strut-based lattice design. This paper presents a modelling framework for implementing a range of both form and surface defects into finite element meshes of strut-based lattices. A signed distance function forms the foundation for this framework, upon which surface meshes can be modified and converted into tetrahedral meshes via open-source software. The paper demonstrates how radius variation, strut waviness, elliptical cross sections and surface defects can be modelled in lattice struts, for which intuitive mathematical definitions are provided. A parametric study is performed to assess the sensitivity of the compressive Young’s modulus of BCCZ and octet-truss lattices to upskin and downskin surface defects. The results showed higher sensitivity in the octet-truss than in the BCCZ; both designs were more sensitive to downskin defects than upskin defects.

Mendelian randomization in the multivariate general linear model framework.

Mendelian randomization (MR) is an application of instrumental variable (IV) methods to observational data in which the IV is a genetic variant. MR methods applicable to the general exponential family of distributions are currently not well characterized. We adapt a general linear model framework to the IV setting and propose a general MR method applicable to any full-rank distribution from the exponential family. Empirical bias and coverage are estimated via simulations. The proposed method is compared to several existing MR methods. Real data analyses are performed using data from the REGARDS study to estimate the potential causal effect of smoking frequency on stroke risk in African Americans. In simulations with binary variates and very weak instruments the proposed method had the lowest median [Q1 , Q3 ] bias (0.10 [-3.68 to 3.62]); compared with 2SPS (0.27 [-3.74 to 4.26]) and the Wald method (-0.69 [-1.72 to 0.35]). Low bias was observed throughout other simulation scenarios; as well as more than 90% coverage for the proposed method. In simulations with count variates, the proposed method performed comparably to 2SPS; the Wald method maintained the most consistent low bias; and 2SRI was biased towards the null. Real data analyses find no evidence for a causal effect of smoking frequency on stroke risk. The proposed MR method has low bias and acceptable coverage across a wide range of distributional scenarios and instrument strengths; and provides a more parsimonious framework for asymptotic hypothesis testing compared to existing two-stage procedures.

Impacts of Climate Change on Blue and Green Water Resources in the Xiangjiang River Basin of the Yangtze River, China

Green water resources, which are fundamental for plant growth and terrestrial ecosystem services, reflect precipitation that infiltrates into the unsaturated soil layer and returns to the atmosphere by plant transpiration and soil evaporation through the hydrological cycle. However, green water is usually ignored in water resource assessments, especially when considering future climate impacts, and green water modeling generally ignores the calibration of evapotranspiration (ET), which might have a considerable impact on green water resources. This study analyzes the spatiotemporal variations in blue and green water resources under historical and future climate change scenarios by applying a distributed hydrological model in the Xiangjiang River Basin (XRB) of the Yangtze River. An improved model calibration method based on remotely sensed MODIS ET data and observed discharge data is used, and the results show that the parallel parameter calibration method can increase the simulation accuracy of blue and green water while decreasing the output uncertainties. The coefficients (p-factor, r-factor, KGE, NSE, R2, and PBIAS) indicate that the blue and green water projections in the calibration and validation periods exhibit good performance. Blue and green water account for 51.9 and 48.1%, respectively, of all water resources in the historical climate scenario, while future blue and green water projections fluctuate to varying degrees under different future climate scenarios because of uncertainties. Blue water resources and green water storage in the XRB will decrease (5.3–21.8% and 8.8–19.7%, respectively), while green water flow will increase (5.9–14.7%). Even taking the 95% parameter prediction uncertainty (95 PPU) range into consideration, the future increasing trend of the predicted green water flow is deemed satisfactory. Therefore, incorporating green water into future water resource management is indispensable for the XRB. In general, this study provides a basis for future blue and green water assessments, and the general modeling framework can be applied to other regions with similar challenges.

Crosscutting Multiscale Modeling of Electrolysis Cells for Accelerating Materials R&D

Numerical models are tools that can be used to a) elucidate fundamental phenomena that are difficult to observe/resolve experimentally, and b) observe device performance as a function of materials properties and operating conditions. The latter use is particularly valuable for informing the design of cell components and accelerating their implementation at practical scales. This presentation will discuss multiple modeling approaches for electrochemical cells and the corresponding computational methods used to solve them. We will describe how high-fidelity models can be used to analyze cell components by assessing their performance, lifetime, and reliability.In our approach, a general framework for electrochemical modeling is constructed using principles of conservation of mass, momentum, charge, energy, and species. Then, application-specific, user-defined source terms are implemented which generally account for chemical and electrochemical reactions. These source terms are translated to all the conservation equations mentioned above, which expands the functionality of the computational fluid dynamics software and allows the basic modeling approach to be very flexible. Through the specific mathematical descriptions for the molecular conversion processes, such as H2 production or CO2 electrolysis, the modeling methods can be readily adapted to various electrochemical cell architectures as a general approach for component and device design or performance optimization.After validating to lab-scale experimental data, the models can be used to perform sensitivity studies on the material properties to predict the most impactful avenues for developing a system component. In addition, existing component designs can be compared to determine which is better suited to a particular application. Ranges of operating conditions can be explored in silico to observe their effect on performance at a much faster rate than can be investigated experimentally. Examples of using this approach in the past include: Analyzing the performance of various thin foil LGDL designs for low temperature proton exchange membrane electrolysis cellsStudying the effect of operating conditions on the leakage current phenomena in proton conducting solid oxide electrolysis cellsInvestigating the role of the thickness of the catholyte buffer layer in low temperature CO2 electrolysis cells These diverse applications demonstrate the usefulness of the generalized modeling framework.This presentation will demonstrate how computational modeling can link experimental materials research with the final component or product design and help close the gap between innovation and implementation. Our approach facilitates materials R&D and advances computational tools to support industry and other high technology readiness level efforts. These insights are used to inform the device design and obtain performance, degradation, and life cycle predictions, which are then used to accelerate material implementation into a finalized product.

Penalized mediation models for multivariate data.

Statistical methods to integrate multiple layers of data, from exposures to intermediate traits to outcome variables, are needed to guide interpretation of complex data sets for which variables are likely contributing in a causal pathway from exposure to outcome. Statistical mediation analysis based on structural equation models provide a general modeling framework, yet they can be difficult to apply to high-dimensional data and they are not automated to select the best fitting model. To overcome these limitations, we developed novel algorithms and software to simultaneously evaluate multiple exposure variables, multiple intermediate traits, and multiple outcome variables. Our penalized mediation models are computationally efficient and simulations demonstrate that they produce reliable results for large data sets. Application of our methods to a study of vascular disease demonstrates their utility to identify novel direct effects of single-nucleotide polymorphisms (SNPs) on coronary heart disease and peripheral artery disease, while disentangling the effects of SNPs on the intermediate risk factors including lipids, cigarette smoking, systolic blood pressure, and type 2 diabetes.

Computational homogenisation based extraction of transverse tensile cohesive responses of cortical bone tissue.

The numerical assessment of fracture properties of cortical bone is important in providing suggestions on patient-specific clinical treatments. We present a generic finite element modelling framework incorporating computational fracture approaches and computational homogenisation techniques. Finite element computations for statistical volume elements (SVEs) at the microscale are performed for different sizes with random osteon packing with a fixed volume fraction. These SVEs are loaded in the transverse direction under tension. The minimal SVE size in terms of ensuring a representative effective cohesive law is suggested to be 0.6 mm. Since cement lines as weak interfaces play a key role in bone fracture, the effects of their fracture properties on the effective fracture strength and toughness are investigated. The extracted effective fracture properties can be used as homogenised inputs to a discrete crack simulation at macroscopic or structural scale. The extrinsic toughening mechanisms observed in the SVE models are discussed with a comparison against experimental observations from the literature, giving beneficial insights to cortical bone failure.

17.3 ASSOCIATIONS BETWEEN CHILDHOOD MALTREATMENT, ALCOHOL USE DISORDER, AND NEURO-COMPUTATIONAL IMPAIRMENTS IN REWARD PREDICTION ERROR (RPE) REPRESENTATION

This part of the Symposium will focus on a series of novel studies that investigate gaps in the current literature on neurocomputational impairments in childhood maltreatment, substance use, and conduct disorder (CD). Prior work has found that trauma exposure is associated with impairments in reward prediction error (RPE) representation in adolescents. Despite the association between trauma and CD, the impact of maltreatment on RPE representation in individuals with CD is unclear. Further, the extent to which maltreatment-related dysfunction in RPE representation relates to alcohol use disorder (AUD) vs cannabis use disorder (CUD) is unclear. A total of 156 adolescents participated in a 3-armed bandit instrumental learning task in which they learn to select novel or nonnovel stimuli associated with a certain monetary value. A mixed reinforcement learning/logistic regression method was used to calculate individual novelty propensity (NP) during the task. Functional MRI data were analyzed within the general linear model framework. In Study 1, maltreatment was measured with the Childhood Trauma Questionnaire (CTQ) in a subsample of adolescents with CD (N = 89). In Study 2, AUD severity was measured with the Alcohol Use Disorders Identification Test (AUDIT), and CUD severity was measured with the Cannabis Use Disorder Identification Test (CUDIT) within the full sample (N = 156). In Study 1, there was CTQ-by-NP interaction on RPE representation during selection of novel stimuli within dorsolateral prefrontal cortex (dlPFC) and inferior frontal gyrus (iFG) (p < 0.05, corrected). In Study 2, AUD severity was associated with alterations in RPE representation within striatum, anterior insular cortex, iFG, dlPFC, and anterior cingulate cortex (ACC), particularly when exploring novel stimuli (p < 0.05, corrected) and with behavioral impairments on the task (p < 0.05). Our findings show that trauma is related to neural representation of RPE within dlPFC and iFG in individuals with CD. These regions also overlap with regions associated with impaired RPE representation in individuals with high AUD severity. Future work should investigate the relationships between maltreatment and AUD in individuals with and without CD.

Economic and environmental impacts of ballast water management on Small Island Developing States and Least Developed Countries

The Ballast Water Management Convention can decrease the introduction risk of harmful aquatic organisms and pathogens, yet the Convention increases shipping costs and causes subsequent economic impacts. This paper examines whether the Convention generates disproportionate invasion risk reduction results and economic impacts on Small Island Developing States (SIDS) and Least Developed Countries (LDCs). Risk reduction is estimated with an invasion risk assessment model based on a higher-order network, and the effects of the regulation on national economies and trade are estimated with an integrated shipping cost and computable general equilibrium modeling framework. Then we use the Lorenz curve to examine if the regulation generates risk or economic inequality among regions. Risk reduction ratios of all regions (except Singapore) are above 99%, which proves the effectiveness of the Convention. The Gini coefficient of 0.66 shows the inequality in risk changes relative to income levels among regions, but risk reductions across all nations vary without particularly high risks for SIDS and LDCs than for large economies. Similarly, we reveal inequality in economic impacts relative to income levels (the Gini coefficient is 0.58), but there is no evidence that SIDS and LDCs are disproportionately impacted compared to more developed regions. Most changes in GDP, real exports, and real imports of studied regions are minor (smaller than 0.1%). However, there are more noteworthy changes for select sectors and trade partners including Togo, Bangladesh, and Dominican Republic, whose exports may decrease for textiles and metal and chemicals. We conclude the Convention decreases biological invasion risk and does not generate disproportionate negative impacts on SIDS and LDCs.

The discrete-time Kermack-McKendrick model: A versatile and computationally attractive framework for modeling epidemics.

The COVID-19 pandemic has led to numerous mathematical models for the spread of infection, the majority of which are large compartmental models that implicitly constrain the generation-time distribution. On the other hand, the continuous-time Kermack-McKendrick epidemic model of 1927 (KM27) allows an arbitrary generation-time distribution, but it suffers from the drawback that its numerical implementation is rather cumbersome. Here, we introduce a discrete-time version of KM27 that is as general and flexible, and yet is very easy to implement computationally. Thus, it promises to become a very powerful tool for exploring control scenarios for specific infectious diseases such as COVID-19. To demonstrate this potential, we investigate numerically how the incidence-peak size depends on model ingredients. We find that, with the same reproduction number and the same initial growth rate, compartmental models systematically predict lower peak sizes than models in which the latent and the infectious period have fixed duration.

Computing Stackelberg Equilibria in Discounted Stochastic Games

Stackelberg games increasingly influence security policies deployed in real-world settings. Much of the work to date focuses on devising a fixed randomized strategy for the defender, accounting for an attacker who optimally responds to it. In practice, defense policies are often subject to constraints and vary over time, allowing an attacker to infer characteristics of future policies based on current observations. A defender must therefore account for an attacker's observation capabilities in devising a security policy. We show that this general modeling framework can be captured using stochastic Stackelberg games (SSGs), where a defender commits to a dynamic policy to which the attacker devises an optimal dynamic response. We then offer the following contributions. 1) We show that Markov stationary policies suffice in SSGs, 2) present a finite-time mixed-integer non-linear program for computing a Stackelberg equilibrium in SSGs, and 3) present a mixed-integer linear program to approximate it. 4) We illustrate our algorithms on a simple SSG representing an adversarial patrolling scenario, where we study the impact of attacker patience and risk aversion on optimal defense policies.

Retaliatory aggressive driving: A justice perspective

Driving anger and roadway aggression have previously been conceptualized using attributional theory, the theory of planned behavior, and the general aggression model (GAM) framework. The current study builds on these findings, testing the applicability of the attribution-of-blame model of perceptions of injustice and expanding existing models of retaliatory driving aggression to include unjust world beliefs and sensitivity to injustice. A sample of 269 participants from a large urban Canadian university viewed five animated driving scenarios (i.e., a queuing violation, a dangerous turn in front of oncoming traffic, selfish parking behavior, misuse of a high occupancy vehicle lane, and a driver failing to stop at a red light). Prior to viewing each scenario, a brief written description of the scenario was provided to each participant and read aloud by the experimenter. After viewing each scenario, participants completed a questionnaire regarding their attributions, emotions, and anticipated behavior in response to the animated scenario. After viewing all animated videos, participants completed a second questionnaire that assessed individual differences and demographic variables. Consistent with the GAM, structural equation and mediation analyses identified a significant path from individual differences (i.e., belief in an unjust world and driving injustice sensitivity), through internal states (i.e., perceptions of injustice and anger), to retaliatory aggressive driving. Results of this study found consistent paths between factors which were significant across all five scenarios and may therefore be generalizable to other driving situations. Other pathways were found to influence only a selection of the five scenarios, suggesting that they may be situation specific. Results provide support for possible intervention strategies that can be employed by driver education programs to reduce aggressive driving.

Mathematics interest, anxiety, self-efficacy and achievement: Examining reciprocal relations

The present study examined the reciprocal relations among mathematics interest (MI), mathematics anxiety (MA), mathematics self-efficacy (MSE) and mathematics achievement of primary school students. Based on longitudinal data from 2789 participants, general latent variable modeling framework was used to explore reciprocal effects. The results indicated that (a) prior mathematics achievement positively predicted later MI, whereas previous MI did not affect subsequent mathematics achievement; (b) there was a bidirectional relationship between MA and mathematics achievement as well as MSE and mathematics achievement; (c) prior MA and MSE significantly predicted later MI, whereas the opposite was not; and (d) MA and MSE were reciprocally linked over time. These research results emphasized the importance of developing students' positive mathematical attitudes, emotions and beliefs and shed light on primary school students' mathematics learning in China.

On skill and chance in sport

AbstractThis work studies outcome uncertainty and competitive balance from a broad perspective. It considers four sports with varying scoring rates, from soccer with typically three goals per match to netball with one hundred goals per match. Within a general modelling framework for a two-competitor contest, we argue that outcome uncertainty, the extent to which the outcome of a contest is unpredictable, depends on scoring rate, on strength variation and on score dependence. Score dependence is essentially the tendency for scores to alternate because possession alternates and possession is advantageous. We regard competitive balance as lack of variation in strength or skill, so that when strength variation is large competitive balance is low and vice versa. Thus, we argue that the outcome of a contest depends on skill, scoring rate, score dependence and chance. This description of outcome is useful because it informs policy-making in sport about the design of scoring systems and the control of competitive imbalance. Broadly, we find that: soccer is relatively competitively unbalanced but outcomes are uncertain because the scoring rate is low; the Australian football league is competitively balanced and so outcomes are uncertain in spite of the high scoring rate in this sport; international rugby matches are relatively neither competitive nor uncertain so that little is left to chance; and netball matches have uncertain outcomes because scores are positively dependent.

The medium amplitude response of nonlinear Maxwell–Oldroyd type models in simple shear

A general framework for Maxwell-Oldroyd type differential constitutive models is examined, in which an unspecified nonlinear function of the stress and rate-of-deformation tensors is incorporated into the well-known corotational version of the Jeffreys model discussed by Oldroyd. For medium amplitude simple shear deformations, the recently developed mathematical framework of medium amplitude parallel superposition (MAPS) rheology reveals that this generalized nonlinear Maxwell model can produce only a limited number of distinct signatures, which combine linearly in a well-posed basis expansion for the third order complex viscosity. This basis expansion represents a library of MAPS signatures for distinct constitutive models that are contained within the generalized nonlinear Maxwell model. We describe a framework for quantitative model identification using this basis expansion, and discuss its limitations in distinguishing distinct nonlinear features of the underlying constitutive models from medium amplitude shear stress data. The leading order contributions to the normal stress differences are also considered, revealing that only the second normal stress difference provides distinct information about the weakly nonlinear response space of the model. After briefly considering the conditions for time-strain separability within the generalized nonlinear Maxwell model, we apply the basis expansion of the third order complex viscosity to derive the medium amplitude signatures of the model in specific shear deformation protocols. Finally, we use these signatures for estimation of model parameters from rheological data obtained by these different deformation protocols, revealing that three-tone oscillatory shear deformations produce data that is readily able to distinguish all features of the medium amplitude, simple shear response space of this generalized class of constitutive models.

Age replacement with Markovian opportunity process

This paper focuses on the age replacement problems under the assumption that the arrival of opportunities follows a stochastic point process. The opportunity is a chance to make the replacement, and one can replace a unit with a low cost at the opportunity. In this paper, the opportunity-based age replacement models by Dekker and Dijkstra (1992) and Zhao and Nakagawa (2012) are extended in the environment where the opportunity process is in accordance with a Markovian arrival process (MAP). The MAP is one of the general point processes, and involves a Poisson process and some renewal process classes. This work introduces the generalization of the arrival process of the preventive replacement problems with opportunities. Furthermore, a comprehensive evaluation of the opportunity-based age replacement policies by Dekker and Dijkstra (1992) and Zhao and Nakagawa (2012) in the generalized modeling framework is carried out.

Multi-scale simulation and dynamic coordination evaluation of water-energy-food and economy for the Pearl River Delta city cluster in China

In this research, an integrated approach is developed through the incorporation of systems dynamics (SD), catastrophe progression (CP), and coupled coordination degree (CCD) analysis within a general modelling framework. The developed SD-CP-CCD is then employed to simulate and evaluate relationships among the water-energy-food (WEF) and the economic systems. It will improve traditional methods for WEF nexus analysis through a) incorporating urban WEF connections and changes into the cross-system coupling analysis framework, b) evaluating its coordination with economic growth and a multi-scale and regional disparity, and c) promoting policy recommendations to ensure the guarantee of urban WEF under economic growth. The approach is then verified through WEF nexus system of Urban Agglomerations of Pearl River Delta City Cluster (PRDCC) in China. Temporal and spatial characteristics of CCD in the region were analyzed. The results revealed their performance in cities with multiple economic backgrounds. Also, the fragile factors of each city were reflected by multi-scale exploration. Regional inequality and spatial agglomeration effects were considered. The results showed that CCD has noticeable temporal and spatial differences. Geographically, CCD varied from uncoordinated to high-level coordination. The eastern cities were much better coordinated than the western cities. Due to the increasing pressure of population and economic growth in the future, the upward trend of CCD would occur in most cities. The vulnerability factors of each city were explored. Simultaneously, apparent spatial inequality and agglomeration patterns were observed, with a downward trend over time. The temporal and spatial patterns of CCD revealed in this study indicated that PRDCC policymakers should formulate policies that suit the characteristics of cities and reduce the targeted regional imbalances.

From drought to deluge: spatiotemporal variation in migration routing, survival, travel time and floodplain use of an endangered migratory fish

We developed a novel statistical model to relate the daily survival and migration dynamics of an endangered anadromous fish to river flow and water temperature during both extreme drought and severe flooding in an intensively managed river system. Our Bayesian temporally stratified multistate mark–recapture model integrates over unobserved travel times and route transitions to efficiently estimate covariate relationships and includes an adjustment for telemetry tag battery failure. We applied the model to acoustic-tagged juvenile Sacramento River winter-run Chinook salmon (Oncorhynchus tshawytscha) and found that survival decreased with decreasing river flows and increased water temperatures. We found that fish were likely to enter a large floodplain during flood conditions and that survival in the floodplain was comparable to the mainstem Sacramento River. Our study demonstrates the response of an endangered anadromous fish population to extreme spatial and temporal variability in habitat accessibility and quality. The general model framework we introduce here can be applied to telemetry of migratory fish through systems with multiple routes to efficiently estimate spatiotemporal variation in survival, travel time, and routing.

An IBD-based mixed model approach for QTL mapping in multiparental populations

Key messageThe identity-by-descent (IBD)-based mixed model approach introduced in this study can detect quantitative trait loci (QTLs) referring to the parental origin and simultaneously account for multilevel relatedness of individuals within and across families. This unified approach is proved to be a powerful approach for all kinds of multiparental population (MPP) designs.Multiparental populations (MPPs) have become popular for quantitative trait loci (QTL) detection. Tools for QTL mapping in MPPs are mostly developed for specific MPPs and do not generalize well to other MPPs. We present an IBD-based mixed model approach for QTL mapping in all kinds of MPP designs, e.g., diallel, Nested Association Mapping (NAM), and Multiparental Advanced Generation Intercross (MAGIC) designs. The first step is to compute identity-by-descent (IBD) probabilities using a general Hidden Markov model framework, called reconstructing ancestry blocks bit by bit (RABBIT). Next, functions of IBD information are used as design matrices, or genetic predictors, in a mixed model approach to estimate variance components for multiallelic genetic effects associated with parents. Family-specific residual genetic effects are added, and a polygenic effect is structured by kinship relations between individuals. Case studies of simulated diallel, NAM, and MAGIC designs proved that the advanced IBD-based multi-QTL mixed model approach incorporating both kinship relations and family-specific residual variances (IBD.MQMkin_F) is robust across a variety of MPP designs and allele segregation patterns in comparison to a widely used benchmark association mapping method, and in most cases, outperformed or behaved at least as well as other tools developed for specific MPP designs in terms of mapping power and resolution. Successful analyses of real data cases confirmed the wide applicability of our IBD-based mixed model methodology.